Analytical Solution of Kinematic Wave Time of Concentration for Overland Flow under Green-Ampt Infiltration
Publication: Journal of Hydrologic Engineering
Volume 21, Issue 3
Abstract
In this paper the well-known kinematic wave equation for computing the time of concentration for impervious surfaces has been extended to the case of pervious hillslopes, accounting for infiltration. An analytical solution for the time of concentration for overland flow on a rectangular plane surface is derived using the kinematic wave equation under the Green-Ampt infiltration. The relative time of concentration is defined as the ratio between the time of concentration of an infiltrating plane and the soil sorptivity time scale, depending on the normalized rainfall intensity and a parameter synthesizing the soil and hillslope characteristics. It is shown that for a more complex case (corresponding to the second domain of solution domain), the time of concentration can also be estimated by two simplified approximate procedures. An error analysis for the time of concentration computed for constant and time-varying infiltration is carried out. Finally, for a hillslope under the Green-Ampt infiltration, the time of concentration obtained by the kinematic wave equation is compared with that computed by a nonlinear storage model. An application of the proposed method for two different soils is shown and discussed.
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Acknowledgments
Research was cofinanced by FFR 2012–2013 granted by Università degli Studi di Palermo. The contribution to the manuscript has to be shared between authors as follows: derivations and applications of the proposed procedure were carried out by the first author; both authors analyzed results and wrote the text. The authors thank Dr. M. Sciacca and the anonymous reviewers for the helpful comments and suggestions made during the revision stage.
References
Agnese, C., Bagarello, V., Baiamonte, G., and Iovino, M. (2011). “Comparing physical quality of forest and pasture soils in a Sicilian watershed.” Soil Sci. Soc. Am. J., 75(5), 1958–1970.
Agnese, C., and Baiamonte, G. (2006). “On the hydrologic response of a hillslope where hortonian runoff is dominant.” Rivista di Ingegneria Agraria, 1, 43–54.
Agnese, C., Baiamonte, G., and Cammalleri, C. (2014). “Modelling the occurrence of rainy days under a typical Mediterranean climate.” Adv. Water Resour., 64, 62–76.
Agnese, C., Baiamonte, G., and Corrao, C. (2001). “A simple model of hillslope response for overland flow generation.” Hydrol. Process., 15(17), 3225–3238.
Agnese, C., Baiamonte, G., and Corrao, C. (2007). “Overland flow generation on hillslopes of complex topography: Analytical solutions.” Hydrol. Process., 21(10), 1308–1317.
Akan, O. (1985). “Similarity solution off overland flow on pervious surface.” J. Hydr. Eng., 1057–1067.
Akan, O. (1986). “Time of concentration of overland flow.” J. Irrig. Drain. Eng., 283–292.
Baiamonte, G., and Agnese, C. (2010). “An analytical solution of kinematic wave equations for overland flow under Green-Ampt infiltration.” J. Agric. Eng., 1, 41–49.
Baiamonte, G., D’Asaro, F., and Grillone, G. (2014). “Simplified probabilistic-topologic model for reproducing hillslope rill network surface runoff.” J. Irrig. Drain Eng., 04014080.
Broadbridge, P., and White, I. (1987). “Time to ponding: Comparison of analytic, quasi-analytic, and approximate predictions.” Water Resour. Res., 23(12), 2302–2310.
Brutsaert, W. (2005). Hydrology: An introduction, Cambridge University Press, Cambridge.
Cundy, T. W., and Tento, S. W. (1985). “Solution to the kinematic wave approach to overland flow routing with rainfall excess given by Philip’s equation.” Water Resour. Res., 21(8), 1132–1140.
De Saint Venant, B. (1871). “Théorie du movement non-permanent des eaux avec application aux crues des revierés et al.’introduction des marées dans leur lit.” Academie des Sciences [Paris] Comptes, 73(148–154), 237–240.
Dunne, T. (1978). “Field studies of hillslope processes.” Hillslope hydrology, M. J. Kirkby, ed., McGraw-Hill, New York, 227–293.
Freeze, R. A. (1972). “Role of subsurface flow in generating surface runoff. 2. Upstream source areas.” Water Resour. Res., 8, 1273–1283.
Giráldez, J. V., and Woolhiser, D. A. (1996). “Analytical integration of the kinematic equation for runoff on a plane under constant rainfall rate and Smith and Parlange infiltration.” Water Resour. Res., 32(11), 3385–3389.
Green, W. H., and Ampt, G. A. (1911). “Studies of soil physics. I: Flow of air and water through soils.” J. Agric. Sci., 4, 1–24.
Henderson, F. M., and Wooding, R. A. (1964). “Overland flow and groundwater flow from a steady rainfall of finite duration.” J. Geophys. Res., 69(8), 1531–1540.
Hewlett, J. D., and Hibbert, A. R. (1967). “Factors affecting the response of small watersheds to precipitation in humid areas.” Int. Symp. on Forest Hydrology, Pergamon Press, Oxford, U.K., 275–290.
Horton, R. E. (1933). “The role of infiltration in the hydrologic cycle.” Eos Trans. Am. Geophys. Union, 14(1), 446–460.
Horton, R. E. (1938). “The interpretation ad application of runoff plane experiments with reference to soil erosion problems.” Soil Sci. Soc. Am. Proc., 1, 401–437.
Larson, C. L. (1965). “A two-phase approach to prediction of peak rates and frequencies of runoff for small ungaged watersheds.” Dept. of Civil Engineering, Stanford Univ., Stanford, CA, 53.
Lighthill, M. J., and Whitham, G. B. (1955). “On kinematic waves. I. Flood movement in long rivers.” Proc. R. Soc. London, Ser. A, 229(1178), 281–316.
Luce, C. H., and Cundy, T. W. (1992). “Modification of the kinematic wave-Philip infiltration overland flow model.” Water Resour. Res., 28(4), 1179–1186.
Raats, P. A. C., and Gardner, W. R. (1971). “Comparison of empirical relationships between pressure head and hydraulic conductivity and some observations on radially symmetric flow.” Water Resour. Res., 7(4), 921–928.
Reggiani, P., Todini, E., and Meißner, D. (2013). “Analytical solution of a kinematic wave approximation for channel routing.” Hydrol. Res., 45(1), 43.
Robinson, J. S., and Sivapalan, M. (1996). “Instantaneous response functions of overland flow and subsurface stormflow for catchment models.” Hydrol. Process., 10(6), 845–862.
Robinson, J. S., and Sivapalan, M., and Snell, J. D. (1995). “On the relative roles of hillslope processes, channel routing, and network geomorphology in the hydrologic response of natural catchment.” Water Resour. Res., 31(12), 3089–3101.
Saghafian, B., and Julien, P. Y. (1995). “Time to equilibrium for spatially variable watersheds.” J. Hydrol., 172(1–4), 231–245.
Singh, V. P. (1976). “Derivation of time of concentration.” J. of Hydrol., 30(1–2), 147–165.
Singh, V. P. (1996). Kinematic-wave modeling in water resources: Surface-water hydrology, Wiley, New York, 1399.
Singh, V. P. (1997). Kinematic-wave modeling in water resources: Environmental hydrology, Wiley, New York, 830.
Smith, R. E., and Parlange, J. Y. (1978). “A parameter-efficient hydrologic infiltration model.” Water Resour. Res., 14(3), 533–538.
Smith, R. E., Smettem, K. R. J., Broadbridge, P., and Woolhiser, D. A. (2002). Infiltration theory for hydrologic applications, water resources monograph series, Softbound AGU, Washington, DC.
Smith, R. E., Wollhiser, D. A. (1971). “Overland flow on infiltrating hillslope.” Wat. Resour. Res., 7(4), 899–913.
White, I., and Sully, M. J. (1987). “Macroscopic and microscopic capillary length and time scales from field infiltration.” Water Resour. Res., 23(8), 1514–1522.
Woolhiser, D. A., and Liggett, J. V. (1967). “Unsteady one-dimensional flow over a plane--the rising hydrograph.” Water Resour. Res., 3(3), 753–771.
Woolhiser, D. A., Smith, R. E., and Giráldez, J. V. (1996). “Effects of spatial variability of saturated hydraulic conductivity on Hortonian overland flow.” Wat. Resour. Res., 32(3), 671–678.
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Published In
Journal of Hydrologic Engineering
Volume 21 • Issue 3 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jan 15, 2015
Accepted: May 14, 2015
Published online: Dec 14, 2015
Published in print: Mar 1, 2016
Discussion open until: May 14, 2016
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